Multi-beam scanning device, multi-beam scanning method, light source device, and image forming apparatus

ABSTRACT

In a multi-beam scanning device and method of the present invention, a semiconductor laser array having a plurality of light emitting parts emitting multiple laser beams is provided. A rotary deflector deflects the laser beams emitted by the light emitting parts of the semiconductor laser array. The deflected laser beams from the rotary deflector is focused onto a scanned surface to form a plurality of beam spots that are separated on the scanned surface in a sub-scanning direction, the scanned surface being scanned simultaneously with the plurality of beam spots in a main scanning direction by a rotation of the rotary deflector. The laser array is configured such that the light emitting parts are arrayed along a line that is at an inclination angle φ to the sub-scanning direction, the inclination angle φ measured in degrees and meeting the conditions )≦φ&lt;90, and that a scanning line pitch P, an array pitch ρ of the light emitting parts of the laser array and a parameter K defined by the equation K=0.82λ/ωz, where λ is a wavelength of the emitted laser beams and ωz is a target beam spot diameter in the sub-scanning direction, satisfy the following conditions:  
     0.01&lt;K·P/(ρ·cos φ)&lt;0.30 0.011&lt;K&lt;0.030.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a multi-beam scanning device, amulti-beam scanning method, and a light source device for use in themulti-beam scanning device. Further, the present invention relates to animage forming apparatus in which the multi-beam scanning device isprovided.

[0003] 2. Description of The Related Art

[0004] With the widespread use of image forming apparatus, such as laserprinters and digital copiers, there is an increasing demand for improvedprinting speeds of the image forming apparatus. To meet the requirement,a multi-beam scanning device having a plurality of light sources isproposed for use in the image forming apparatus. In the multi-beamscanning device, the plurality of light sources, such as laser diodes,are used to emit multiple light beams for scanning the scanned surfacewith the multiple light spots at a time. For example, a multi-beamscanning device using a semiconductor laser array as the plurality oflight sources is known.

[0005] When the optical scanning is performed on a scanned surface of aphotosensitive medium at a higher density (e.g., above 600 dpi) with themulti-beam scanning device, the pitch of the scanning lines is decreasedto a smaller level to achieve the high-density scanning, and thediameter of beam spots on the photosensitive medium surface in thesub-scanning direction must be decreased accordingly. A beam spot isformed on the scanned surface by the focused laser beam from the lightsource. The scanned surface that is actually scanned with the focusedlaser beam does not necessarily accord with an image surface where thebeam spot is precisely formed at the waist of the laser beam due to thefield curvature of the focusing lens or the like of the optical scanningdevice. The diameter of the beam spot on the scanned surface is notnecessarily equal to the beam waist diameter. To reduce the variation ofthe beam spot diameter as much as possible, the correction of the fieldcurvature of the focusing lens is carried out.

[0006] Further, optical scanning devices after assembly contain severalkinds of errors, regardless of whether they are the multi-beam scanningdevice or the single-beam scanning device. Such errors includerespective errors of the component parts of the optical scanning device,an assembly error of the optical scanning device, and others. When sucherrors exist in the optical scanning device, the beam spot formed on thescanned surface with the light beam from the optical scanning device isin a defocus state. The scanned surface that is actually scanned withthe focused laser beam is liable to variations of the image surface.

[0007] By taking the above matters into consideration, it is necessarythat the designing of a multi-beam scanning device be based on theassumption that the beam spot on the scanned surface is in a defocusstate. In most cases, the multi-beam scanning device is designed suchthat the variations of the beam spot diameter fall within a range of±10% of a target beam spot diameter “W”. Namely, the beam spot diameter,which is provided by the multi-beam scanning device, is in a range from0.9 W to 1.1 W, where W is a target beam spot diameter.

[0008] When the beam spot on the scanned surface is in a defocus state,the beam spot diameter is larger than the beam waist diameter. Indesigning the optical systems of the multi-beam scanning device, thepractical measure is to determine a permissible beam spot diameter thatis smaller than the target beam spot diameter by 1 to 10 percents. Arange of the defocus amount in which the variations of the beam spotdiameter are less than the above-mentioned permissible beam spotdiameter is called a depth clearance. When the depth clearance is large,the degree of allowance for the variations of the scanned surface to theimage surface is high. It is known from practical experience that thedepth clearance that is above 0.9 mm is needed to eliminate thecomponent part errors or the assembly errors.

[0009] Moreover, in the conventional multi-beam scanning device, thedivergence angle of laser beams emitted by the semiconductor laser arrayis liable to variations. Generally, a semiconductor laser as in thesemiconductor laser array emits a divergent laser beam. The divergenceangle is at the maximum in the direction of thickness of the activatedlayer of the semiconductor laser and at the minimum in the directionperpendicular to the activated layer. The far-field pattern of suchlaser beam is in the form of an ellipse having a major axis parallel tothe direction of thickness of the activated layer. In the semiconductorlaser array described above, the respective divergence angles of thelaser beams emitted by the plurality of light emitting parts are notcommon, and the divergence angle for each of the plurality of lightemitting parts is liable to variations. Hence, the diameters of beamspots, which are formed on the scanned surface by the conventionalmulti-beam scanning device, are also liable to variations due to thevariations of the divergence angles. This causes the degradation of thequality of a reproduced image.

SUMMARY OF THE INVENTION

[0010] In order to overcome the above-described problems, it is anobject of the present invention to provide a multi-beam scanning devicethat ensures adequate depth clearance even when the optical scanning isperformed at a high density above 600 dpi, and effectively reduces thevariations of the beam spots on the scanned surface to a smallestpossible level so that the multi-beam scanning is carried out withaccurate beam spot diameter so as to create good quality of a reproducedimage.

[0011] Another object of the present invention is to provide amulti-beam scanning method that ensures adequate depth clearance evenwhen the optical scanning is performed at a high density above 600 dpi,and effectively reduces the variations of the beam spots on the scannedsurface to a smallest possible level so that the multi-beam scanning iscarried out with accurate beam spot diameter so as to create goodquality of a reproduced image.

[0012] Another object of the present invention is to provide a lightsource device for use in a multi-beam scanning device that ensuresadequate depth clearance even when the optical scanning is performed ata high density above 600 dpi, and effectively reduces the variations ofthe beam spots on the scanned surface to a smallest possible level sothat the multi-beam scanning is carried out with accurate beam spotdiameter so as to create good quality of a reproduced image.

[0013] Another object of the present invention is to provide an imageforming apparatus in which a multi-beam scanning device is provided, themulti-beam scanning device ensuring adequate depth clearance even whenthe optical scanning is performed at a high density above 600 dpi, andeffectively reducing the variations of the beam spots on the scannedsurface to a smallest possible level so that the multi-beam scanning iscarried out with accurate beam spot diameter so as to create goodquality of a reproduced image.

[0014] The above-mentioned objects of the present invention are achievedby a multi-beam scanning device comprising: a semiconductor laser arraywhich has a plurality of light emitting parts emitting multiple laserbeams; a rotary deflector which deflects the laser beams emitted by thelight emitting parts of the semiconductor laser array; and a focusingoptical system which focuses the deflected laser beams from the rotarydeflector onto a scanned surface to form a plurality of beam spots thatare separated on the scanned surface in a sub-scanning direction, thescanned surface being scanned simultaneously with the plurality of beamspots in a main scanning direction by a rotation of the rotarydeflector, wherein the laser array is configured such that the lightemitting parts are arrayed along a line that is at an inclination angleφ to the sub-scanning direction, the inclination angle φ measured indegrees and meeting the conditions 0≦φ<90, and that a scanning linepitch P, an array pitch ρ of the light emitting parts of the laser arrayand a parameter K defined by the equation K=0.82 λ/ωz, where λ is awavelength of the emitted laser beams and ωz is a target beam spotdiameter in the sub-scanning direction, satisfy the followingconditions:

[0015] 0.01<K·P/(ρ·cos )<0.30 0.011<K<0.030.

[0016] The above-mentioned objects of the present invention are achievedby a multi-beam scanning method that comprising the steps of: providinga semiconductor laser array having a plurality of light emitting partsemitting multiple laser beams; providing a rotary deflector deflectingthe laser beams emitted by the light emitting parts of the semiconductorlaser array; focusing the deflected laser beams from the rotarydeflector onto a scanned surface to form a plurality of beam spots thatare separated on the scanned surface in a sub-scanning direction; andscanning the scanned surface simultaneously with the plurality of beamspots in a main scanning direction by a rotation of the rotarydeflector, wherein the laser array is configured such that the lightemitting parts are arrayed along a line that is at an inclination angleφ to the sub-scanning direction, the inclination angle φ measured indegrees and meeting the conditions 0≦φ<90, and that a scanning linepitch P, an array pitch ρof the light emitting parts of the laser arrayand a parameter K defined by the equation K=0.82λ/ωz, where λ is awavelength of the emitted laser beams and ωz is a target beam spotdiameter in the sub-scanning direction, satisfy the followingconditions:

[0017] 0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0.030.

[0018] The above-mentioned objects of the present invention are achievedby a light source device for use in a multi-beam scanning device, thelight source device comprising: a semiconductor laser array which has aplurality of light emitting parts emitting multiple laser beams; acoupling lens which couples the laser beams emitted by the laser array;and an aperture stop which restricts a diameter of the laser beamspassed through the coupling lens, wherein the multi-beam scanning devicecomprises: the light source device; a rotary deflector which deflectsthe laser beams emitted by the light emitting parts of the laser array;and a focusing optical system which focuses the deflected laser beamsfrom the rotary deflector onto a scanned surface to form a plurality ofbeam spots that are separated on the scanned surface in a sub-scanningdirection, the scanned surface being scanned simultaneously with theplurality of beam spots in a main scanning direction by a rotation ofthe rotary deflector, wherein the laser array is configured such thatthe light emitting parts are arrayed along a line that is at aninclination angle φ to the sub-scanning direction, the inclination angleφ measured in degrees and meeting the condition 0≦φ<90, and that ascanning line pitch P, an array pitch ρ of the light emitting parts ofthe laser array and a parameter K defined by the equation K=0.82 λ/ωz,where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions:

[0019] 0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0.030

[0020] and wherein the aperture stop is configured to have a numericalaperture NAzS in the sub-scanning direction that satisfies theconditions: 0.01<NAzS<0. 30.

[0021] The above-mentioned objects of the present invention are achievedby an image forming apparatus in which a multi-beam scanning device isprovided, the image forming apparatus forming an electrostatic latentimage on a scanned surface of a photosensitive medium through anexposure of the photosensitive medium to an imaging light patternprovided by the multi-beam scanning device, the multi-beam scanningdevice including: a semiconductor laser array which has a plurality oflight emitting parts emitting multiple laser beams; a rotary deflectorwhich deflects the laser beams emitted by the light emitting parts ofthe semiconductor laser array; and a focusing optical system whichfocuses the deflected laser beams from the rotary deflector onto ascanned surface to form a plurality of beam spots that are separated onthe scanned surface in a sub-scanning direction, the scanned surfacebeing scanned simultaneously with the plurality of beam spots in a mainscanning direction by a rotation of the rotary deflector, wherein thelaser array is configured such that the light emitting parts are arrayedalong a line that is at an inclination angle φ to the sub-scanningdirection, the inclination angle φ measured in degrees and meeting theconditions 0<φ<90, and that a scanning line pitch P, an array pitch ρ ofthe light emitting parts of the laser array and a parameter K defined bythe equation K=0.82 λ/ωz, where λ is a wavelength of the emitted laserbeams and ωz is a target beam spot diameter in the sub-scanningdirection, satisfy the following conditions:

[0022] 0.01<K·P(ρ·cos φ)<0.30 0.011<K<0.030.

[0023] In the multi-beam scanning device and method of the presentinvention, the semiconductor laser array is used as the plurality oflight sources and it is possible to ensure adequate depth clearance whenthe optical scanning is performed at a high density. The multi-beamscanning device and method of the present invention are effective inreducing the variations of the beam spots on the scanned surface, sothat the multi-beam scanning is carried out with accurate beam spotdiameter so as to create good quality of a reproduced image. Therefore,the image forming apparatus in which the multi-beam scanning device ofthe present invention is provided can create good quality of areproduced image.

BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Other objects, features and advantages of the present inventionwill be apparent from the following detailed description when read inconjunction with the accompanying drawings.

[0025]FIG. 1 is a perspective view of one preferred embodiment of themulti-beam scanning device of the present invention.

[0026]FIG. 2 is a diagram for explaining a sub-scanning-directionimaging pattern of a light beam between one of the light emitting partsof a light source unit and the scanned surface of a photosensitivemedium.

[0027]FIG. 3A, FIG. 3B, FIG. 3C and FIG. 3D are diagrams for explaininga relationship between the semiconductor laser array, the aperture stop,and the far-field pattern.

[0028]FIG. 4 is a diagram for explaining a configuration of the opticalsystems of a first preferred embodiment of the multi-beam scanningdevice.

[0029]FIG. 5A and FIG. 5B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 4.

[0030]FIG. 6 is a diagram for explaining a configuration of the opticalsystems of a second preferred embodiment of the multi-beam scanningdevice.

[0031]FIG. 7A and FIG. 7B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 6.

[0032]FIG. 8 is a diagram for explaining a configuration of the opticalsystems of a third preferred embodiment of the multi-beam scanningdevice.

[0033]FIG. 9A and FIG. 9B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 8.

[0034]FIG. 10 is a diagram for explaining a configuration of the opticalsystems of a fourth preferred embodiment of the multi-beam scanningdevice.

[0035]FIG. 11A and FIG. 11B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 10.

[0036]FIG. 12A and FIG. 12B are diagrams for explaining a configurationof the optical systems of a fifth preferred embodiment of the multi-beamscanning device.

[0037]FIG. 13A and FIG. 13B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 12A and FIG. 12B.

[0038]FIG. 14 is a diagram for explaining a configuration of the opticalsystems of a sixth preferred embodiment of the multi-beam scanningdevice.

[0039]FIG. 15A and FIG. 15B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 14.

[0040]FIG. 16 is a diagram for explaining one preferred embodiment ofthe image forming apparatus of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0041] A description will be given of preferred embodiments of themulti-beam scanning device and the image forming apparatus of thepresent invention with reference to the accompanying drawings.

[0042]FIG. 1 is a perspective view of one preferred embodiment of themulti-beam scanning device of the present invention.

[0043] The multi-beam scanning device of the present embodiment isprovided for use in an image forming apparatus, such as a laser printer,a digital copier or a laser facsimile. In the image forming apparatus,an image is formed on a scanned surface of a photosensitive medium whenthe photosensitive medium surface is scanned in a main scanningdirection and a sub-scanning direction by the laser beams focused by themulti-beam scanning device.

[0044] Specifically, the multi-beam scanning device of the presentembodiment is provided for use in an image forming apparatus that formsan image through an electrophotographic printing process. In theelectrophotographic printing process, there are basically six majorsteps employed: (1) charging of the photosensitive medium; (2) exposingof the photosensitive medium to the imaging light pattern; (3)developing of the photosensitive medium with toner; (4) transferring ofthe toned image from the photosensitive medium to the final medium(usually paper); (5) thermal fusing of the toner to the paper; and (6)cleaning of residual toner from the photosensitive medium surface. Theoptical scanning of the photosensitive medium surface, which isperformed by the laser beams from the multi-beam scanning device of theabove-described embodiment, corresponds to the exposing step of theelectrophotographic printing process that is carried out by the imageforming apparatus.

[0045] As shown in FIG. 1, the multi-beam scanning device of the presentembodiment generally comprises a semiconductor laser diode (or a lightsource unit) 1, a coupling lens 2, an aperture stop 3, a line focusinglens 4, a rotary polygonal mirror 5, an fθ lens 6, an elongated focusinglens 7, a reflector mirror 8, a photosensitive belt 9, and a syncmonitoring detector. The sync monitoring device includes a mirror 10, afocusing lens 11 and a sync monitoring sensor 12. The sync monitoringsensor 12 is formed by, for example, a photodiode, and the syncmonitoring sensor 12 converts the incident light beam into a sync signalthat is indicative of a time the sync monitoring sensor 12 has receivedthe light beam from the light source unit 1.

[0046] The light source device according to one embodiment of thepresent invention is constituted by the semiconductor laser array 1, thecoupling lens 2, and the aperture stop 3 in the multi-beam scanningdevice of FIG. 1. The light source device may be configured into asingle device that includes the elements 1, 2 and 3 of the multi-beamscanning device of FIG. 1.

[0047] In the multi-beam scanning device of FIG. 1, the semiconductorlaser array 1 includes a plurality of light emitting parts that emit aplurality of divergent laser beams in accordance with an image signal(which carries imaging information). The laser beams from thesemiconductor laser array 1 are directed to the coupling lens 2. Thecoupling lens 2 couples the laser beams emitted by the semiconductorlaser array 1, and introduces the coupled laser beams into the aperturestop 3. The aperture stop 3 restricts the diameter of the incident laserbeams to an appropriate level, and introduces the laser beams into theline focusing lens 4.

[0048] The line focusing lens 4 provides a refraction power to the laserbeams, passed through the aperture stop 3, with respect to only thesub-scanning direction. The line focusing lens 4 is formed by, forexample, a cylindrical lens. With the refraction power of the focusinglens 4, the laser beams from the aperture stop 4 form line images at anadjacent position of the rotary polygonal mirror 5, which are elongatedin the main scanning direction and separated from each other in thesub-scanning direction.

[0049] The rotary polygonal mirror 5 in the present embodiment is arotary deflector having reflection surfaces on the six peripheral sides.One of the reflection surfaces of the rotary polygonal mirror 5 deflectsthe laser beams from the focusing lens 4 while the rotary polygonalmirror 5 is rotated at a constant speed around its rotation axis in therotation direction indicated by the arrow in FIG. 1, which allows thescanned surface to be scanned at a constant speed in the main scanningdirection with the beam spots.

[0050] The deflected laser beams from the polygonal mirror 5 are passedthrough the fθ lens 6 and the elongated focusing lens 7, and the laserbeams from the focusing lens 7 are reflected to the photosensitive belt9 by the reflector mirror 8. The fθ lens 6 and the elongated focusinglens 7 form a focusing optical system in the multi-beam scanning deviceof the present embodiment. With the rotation of the rotary deflector 5,the laser beams from the reflector mirror 8 scan a scanned surface ofthe photosensitive belt 9 in the main scanning direction. This mainscanning direction is parallel to the axial direction of a transportroller that is provided to rotate or transport the photosensitive belt 9around the rotation axis of the transport roller.

[0051] In a synchronous manner with a time the main scanning isperformed (or every time the laser beams from the rotary deflector 5 areincident to the sync monitoring device), the photosensitive belt 9 isrotated around the rotation axis of the transport roller by a givenrotational angle. This causes the photosensitive medium surface to bescanned in the sub-scanning direction by the laser beams focused by themulti-beam scanning device. The sub-scanning direction, which isparallel to the direction in which the photosensitive belt 9 istransported, is perpendicular to the axial direction of the transportroller of the photosensitive belt 9. Therefore, the photosensitivemedium surface is scanned in the main scanning direction and in thesub-scanning direction by the laser beams focused by the multi-beamscanning device. Each of the respective light emitting parts of thesemiconductor laser array 1 is independently turned on and off inaccordance with the image signal, and an electrostatic latent image isformed on the photosensitive medium surface as a result of the exposureof the photosensitive belt 9 to the imaging light pattern provided bythe semiconductor laser array 1.

[0052] In the multi-beam scanning device of FIG. 1, the semiconductorlaser array 1 includes the plurality of light-emitting parts that areindependently turned on and off in accordance with the image signal. Thelaser beams emitted by the light emitting parts of the semiconductorlaser array 1 are focused on the photosensitive medium surface so thatthe respective light spots are formed thereon. The photosensitive mediumsurface is scanned at a substantially constant speed in the mainscanning direction by the laser beams, focused by the multi-beamscanning device, with the rotation of the rotary deflector 5.

[0053] The coupling lens 2 may be configured to convert the laser beamsemitted by the semiconductor laser array 1 into substantially parallellaser beams. Alternatively, the coupling lens 2 may be configured toconvert the laser beams emitted by the semiconductor laser array 1 intoless divergent laser beams. Alternatively, the coupling lens 2 may beconfigured to convert the laser beams emitted by the semiconductor laserarray 1 into convergent laser beams.

[0054] In the multi-beam scanning device of FIG. 1, the sync monitoringdevice is provided to synchronize the timing of a start of every mainscanning of the photosensitive medium surface. As described above, everytime the laser beams from the rotary deflector 5 are incident to thesync monitoring sensor 12, the sync monitoring sensor 12 outputs a syncsignal, and this sync signal is used to start the main scanning of themulti-beam scanning device.

[0055] The sync monitoring device in the present embodiment includes themirror 10, the focusing lens 11 and the sync monitoring sensor 12. Themirror 10 reflects the laser beams, which are sent by the rotarydeflector 5 through the fθ lens 6, to the focusing lens 11. The focusinglens 11 converts the laser beams into convergent laser beams andintroduces them into the sync monitoring sensor 12. The sync monitoringsensor 12 is formed by a photodiode or a charge-coupled device, and thesync monitoring sensor 12 outputs a sync signal upon the receiving ofthe laser beams from the rotary deflector 5. The photosensitive belt 9is rotated around the rotation axis by the given rotational angle insynchronism with the sync signal output by the sync monitoring sensor12.

[0056] In the multi-beam scanning device of FIG. 1, the semiconductorlaser array 1 is provided as the light source unit that emits aplurality of laser beams. The semiconductor laser array 1 includes aplurality of light emitting parts “ch1” through “ch4” (in thisembodiment, the number of the light emitting parts in the light sourcedevice is equal to 4), and these light emitting parts are arrayed alonga line at equal distances. The semiconductor laser array 1 may beconfigured so that the light emitting parts “ch1” through “ch4” arearrayed at equal distances along a slanted line that is inclined at anangle φ (φ>0) to the sub-scanning direction. Hereinafter, this angle φwill be called the inclination angle φ.

[0057]FIG. 2 shows a sub-scanning-direction imaging pattern of the laserbeam from one of the light emitting parts of the semiconductor laserarray 1 to the scanned surface of the photosensitive belt 9.

[0058] In FIG. 2, the sub-scanning direction is parallel to the rotationaxis of the rotary polygonal mirror 5, and the main scanning directionis perpendicular to the plane of FIG. 2.

[0059] In the imaging pattern of the laser beam shown in FIG. 2, thedivergent laser beam is emitted by one of the light emitting parts “ch1”through “ch4” of the semiconductor laser array 1. The coupling lens 2couples the laser beam emitted by the semiconductor laser array 1. Theaperture stop 3 restricts the diameter of the incident laser beam to theappropriate level and introduces the laser beam into the focusing lens4.

[0060] With the refraction power of the focusing lens 4, the laser beamfrom the aperture stop 4 forms a line image at the position adjacent tothe rotary polygonal mirror 5, the line image being elongated in themain scanning direction. In the imaging pattern of FIG. 2, the lineimage formed by the focusing lens 4 is shown as a point on thereflection surface of the rotary polygonal mirror 5.

[0061] The reflection surface of the rotary polygonal mirror 5 deflectsthe laser beam from the focusing lens 4 while the rotary polygonalmirror 5 is rotated at a constant speed around its rotation axis in therotating direction (indicated by the arrow in FIG. 1).

[0062] The deflected laser beam from the rotary polygonal mirror 5 ispassed through the focusing optical system (which is indicated byreference numeral 6A in FIG. 2) that includes the fθ lens 6 and theelongated focusing lens 7, and the laser beam from the focusing opticalsystem 6A is reflected to the surface of the photosensitive belt 9 bythe reflector mirror 8.

[0063] With the focusing action of the focusing optical system 6A, thelaser beam from the focusing optical system 6A forms a beam spot on thesurface of the photosensitive belt 9, the beam spot having a diameter ωzin the sub-scanning direction.

[0064] In the imaging pattern of FIG. 2, suppose that the aperture stop3, which restricts the diameter of the laser beam from the coupling lens2, is configured to have a source-side numerical aperture “NAzS” withrespect to the sub-scanning direction and the focusing optical system6A, facing the scanned surface of the photosensitive belt 9, isconfigured to have an image-side numerical aperture “NAzI” with respectto the sub-scanning direction.

[0065] The multi-beam scanning device of the present embodiment isconfigured such that the beam spot diameter ωz in the sub-scanningdirection is represented by the following formula:

ωz=0.82λ/NAzI  (1)

[0066] where λ is a wavelength of the laser beam emitted by thesemiconductor laser array 1, and NAzI is a numerical aperture of thefocusing optical system 6A with respect to the sub-scanning direction.

[0067]FIG. 3A, FIG. 3B, FIG. 3C and FIG. 3D are diagrams for explaininga relationship between the semiconductor laser array 1, the aperturestop 3 and the far-field pattern.

[0068]FIG. 3A shows a configuration of the semiconductor laser array 1of the present embodiment. As shown in FIG. 3A, the semiconductor laserarray 1 is configured such that the light emitting parts (whichcorrespond to the light emitting parts “ch1” through “ch4” in FIG. 1)are arrayed along a slanted line that is at an inclination angle φ tothe sub-scanning direction of the laser beam incident to the scannedsurface of the photosensitive medium.

[0069] The inclination angle λ is measured in degrees and meets theconditions 0≦φ<90.

[0070] As shown in FIG. 3A, in the present embodiment, asub-scanning-direction array pitch of the light emitting parts in thesemiconductor laser array 1, measured along the vertical line parallelto the sub-scanning direction, is represented by “ρ·cos φ” where ρ is anarray pitch of the light emitting parts of the laser array 1 along theslanted line and φ is the inclination angle of the light emitting partsof the semiconductor laser array 1.

[0071] In the present embodiment, a scanning line pitch P, which is adistance between the main scanning lines on the scanned surface of thephotosensitive medium 9, is determined by an optical writing density(measured in “dpi”, or dots per inch) of the multi-beam scanning device.Suppose that the optical systems between the laser array 1 and thescanned surface of the photosensitive medium 9 have a composite focusingfactor βz in the sub-scanning direction.

[0072] In the multi-beam scanning device of the present embodiment, itis necessary to meet the following equation:

βz=P/(ρ·cos φ)  (2)

[0073] Suppose that the aperture stop 3 has the source-side numericalaperture NAzS with respect to the sub-scanning direction and thefocusing optical system 6A has the image-side numerical aperture NAzIwith respect to the sub-scanning direction, as shown in FIG. 2. Themulti-beam scanning device of the present embodiment meets the followingequation:

NAzS=zNAzI  (3)

[0074] Substituting the equations (1) and (2) into the equation (3)yields the following equation:

NAzS={P/(ρ·cos φ)}{0.82λ/ωz}  (4)

[0075] Suppose that a parameter K is defined by the equation:K=0.82λ/ωz, where λ is a wavelength of the emitted laser beams and ωz isa target beam spot diameter in the sub-scanning direction. The aboveequation (4) is rewritten into the following equation:

NAzS=K·P/(ρ·cos φ)  (4′)

[0076] As is apparent from the FIG. 2, the aperture stop 3 is configuredto have the source-side numerical aperture NAzS with respect to thesub-scanning direction.

[0077] If the numerical aperture NAzS of the aperture stop 3 is notproperly set, the multi-beam scanning device will have the followingproblems. When the aperture stop 3 is configured to have a too smallnumerical aperture NAzS, the multi-beam scanning device is difficult toperform a high-speed optical scanning due to insufficient light energy.On the other hand, when the aperture stop 3 is configured to have a toolarge numerical aperture NAzS, the multi-beam scanning device is liableto variations of the divergence angle for each of the respective beamspots on the scanned surface.

[0078] In the multi-beam scanning device of the present embodiment, thevalue of the parameter K(=0.82λ/ωz) is determined by the wavelength λ ofthe emitted laser beams and the target beam spot diameter ωz in thesub-scanning direction. The value of the parameter K is related to theabove-described depth clearance in the sub-scanning direction.

[0079] Suppose that the wavelength λ ranges from 400 nm to 800 nm andthe target beam spot diameter ωz ranges from 16 μm to 160 μm. Thefollowing table is the results of calculations of the parameter K andthe depth clearance W corresponding to such values of the wavelength λand the target beam spot diameter ωz. λ (nm) ωz (μm) K W (mm) 800 220.0298 0.90 800 50 0.0131 4.65 800 60 0.0109 6.69 780 22 0.0291 0.92 78030 0.0213 1.72 780 50 0.0128 4.77 400 16 0.0205 0.95 400 30 0.0109 3.35

[0080] It is known from practical experience that the depth clearance Wthat is above 0.9 mm is needed to eliminate the component part errors orthe assembly errors. Accordingly, as long as the supposition that thewavelength λ ranges from 400 nm to 800 nm and the target beam spotdiameter ωz ranges from 16 μm to 160 μm is made, the multi-beam scanningdevice of the present embodiment is configured such that the parameter Ksatisfies the following conditions:

0.011<K<0.030  (5)

[0081] The upper limit of the source-side numerical aperture NAzS mustbe determined by taking into consideration the elimination of thevariations of the divergence angle for each of the respective beam spotson the scanned surface.

[0082]FIG. 3B, FIG. 3C and FIG. 3D respectively show the relationshipbetween the laser beam condition at the aperture stop 3 and thefar-field pattern when the inclination angle φ is equal to 0, 45 and 90degrees.

[0083] The divergence angle θ of the divergent laser beam emitted fromthe light emitting part of the laser array 1 when the beam power isabove ½ of the peak value of the power distribution is larger than atleast 20 degrees. As shown in FIG. 3B through FIG. 3D, in a case of theinclination angle φ=0 (FIG. 3B), the divergence angle θ in thesub-scanning direction is minimum.

[0084] Accordingly, the multi-beam scanning device of the presentembodiment is configured such that the numerical aperture NAzS of theaperture stop 3 satisfies the following condition:

NAzS≦sin[tan⁻¹{{square root}{square root over ()}[(2/1n2)tan(θ/2)]}]  (6)

[0085] When the divergence angle θ is equal to 20 degrees, the aboveformula (6) is written into

NAzS≦0.30  (6′)

[0086] In practical applications, the multi-beam scanning device may beconfigured to satisfy the above condition (6′).

[0087] The lower limit of the source-side numerical aperture NAzS mustbe determined by taking into consideration the composite focusing factorβz of the optical systems between the laser array 1 and the scannedsurface 9 in the sub-scanning direction. Specifically, this compositefocusing factor βz is calculated by a product of a lateral magnificationfactor |β1| of the optical systems (the coupling lens 2 and thecylindrical lens 4) between the laser array 1 and the rotary deflector 5in the sub-scanning direction and a lateral magnification factor |β2| ofthe optical systems (the fθ lens 6 and the elongated focusing lens 7) ofthe focusing optical system 6A in the sub-scanning direction. Namely,the composite focusing factor βz of the optical systems between thelaser array 1 and the scanned surface 9 in the sub-scanning direction iscalculated in accordance with the equation βz=|β1|·|β2|.

[0088] It is known from practical experience that the lower limit of|β1| is above 1.8. Namely, |β1|≧1.8. When |β1|<1.8, the location of thecylindrical lens 4 is too close to the rotary deflector 5, and it isdifficult to install the cylindrical lens 4 and the rotary deflector 5with no interference. To avoid the interference between the cylindricallens 4 and the rotary deflector 5 and ensure an adequate lateralmagnification factor, it is necessary to enlarge the distance of thecoupling lens 2 and the laser array 1. However, if the distance isenlarged, the coupling lens 2 can couple only a very small lightquantity of the laser beams from the laser array 1 and the multi-beamscanning device is liable to insufficient light energy.

[0089] Further, it is known from practical experience that the effectiverange of the lateral magnification factor |β2| of the optical systems ofthe focusing optical system 6A in the sub-scanning direction is0.5≦|β2|≦2.0. When |β2|≦0.5, installing the focusing lens 7 at aposition that is very close to the scanned surface 9 is required. Thelength of the focusing lens 7 in the main scanning direction must beincreased and the manufacturing process of such focusing lens 7 becomesexpensive. When |β2|≦2, 0, the variations of the image surface positioncaused by the assembly errors or the like are increased, which causesthe multi-beam scanning device to be difficult to perform the multi-beamscanning at a higher density above 600 dpi.

[0090] From the foregoing considerations, the lower limit of thecomposite focusing factor βz(=|β1|·|β2|) is determined as being about0.9(=1.8×0.5).

[0091] From the above formulas (2) and (4′), the equation NAzS=βz·K isobtained. As the lower limit of the parameter K is 0.011, thesource-side numerical aperture NAzS of the aperture stop 3 must satisfythe following condition:

NAzS≧0.01  (7)

[0092] From the above formulas (6′) and (7),

0.01≦NAzS≦0.30  (8)

[0093] By using the above equation (4′): NAzS=K·P/(ρ·cos φ),

0.01<K·P/(ρ·cos φ)<0.30  (9)

[0094] Accordingly, the multi-beam scanning device of the presentembodiment is configured such that the above conditions (9) aresatisfied.

[0095] Suppose that the wavelength λ ranges from 400 nm to 800 nm andthe target beam spot diameter ωz is set to 30 μm. The following table isthe results of calculations of the parameter K and the depth clearance Wcorresponding to such values of the wavelength λ and the target beamspot diameter ωz. λ (nm) ωz (μm) K W (mm) 800 30 0.022 1.67 780 30 0.0211.72 700 30 0.019 1.91 600 30 0.016 2.23 550 30 0.015 2.43 500 30 0.0142.68 450 30 0.012 2.97 400 30 0.011 3.35

[0096] It is readily understood from the above table that, when thetarget beam spot diameter ωz is set to the same value (30,μm), the thewavelength λ, the larger the depth clearance W. When the wavelength λ isset to a small value, the depth clearance W becomes large and theaccuracy requirements of the optical systems become easy to satisfy.Therefore, it is possible to make the multi-beam scanning device of thepresent embodiment inexpensive. Further, when the wavelength λ is set toa small value, the numerical aperture NAzS can be set to a small value.Hence, the multi-beam scanning device of the present embodiment iseffective in eliminating the variations of the divergence angle.

[0097] From the forgoing considerations, it is preferred that themulti-beam scanning device of the present embodiment is configured suchthat the wavelength A of the emitted laser beams is below 700 nm.

[0098] As described above with reference to FIG. 1 and FIG. 2, in themulti-beam scanning device of the present embodiment, the semiconductorlaser array 1 is configured such that the light emitting parts arearrayed along a line that is at the inclination angle φ to thesub-scanning direction, the inclination angle φ measured in degrees andmeeting the conditions 0≦φ<90, and that the scanning line pitch P, thearray pitch ρ of the light emitting parts of the laser array 1 and theparameter K defined by the equation K=0.82λ/ωz, where λ is thewavelength of the emitted laser beams and ωz is the target beam spotdiameter in the sub-scanning direction, satisfy the followingconditions:

0.01<K·P/(ρ·cos φ)<0.30  (9)

0.011<K<0.030  (5)

[0099] According to the above configuration, the multi-beam scanningdevice and method of the present embodiment can achieve the depthclearance that is above 0.9 mm. Therefore, it is possible to ensureadequate depth clearance when the optical scanning is performed at ahigh density. The multi-beam scanning device and method of the presentembodiment are effective in reducing the variations of the beam spots onthe scanned surface, so that the multi-beam scanning is carried out withaccurate beam spot diameter so as to create good quality of a reproducedimage. Therefore, the image forming apparatus in which the multi-beamscanning device of the present invention is provided can create goodquality of a reproduced image.

[0100] Further, in the multi-beam scanning device of the presentembodiment according to the above configuration, the coupling lens 2couples the laser beams emitted by the laser array 1. The aperture stop3 restricts the diameter of the laser beams passed through the couplinglens 2. The line focusing lens 4 provides a refraction power to thelaser beams, passed through the aperture stop 3, with respect to onlythe sub-scanning direction. The rotary deflector 5 includes thereflection surfaces, the rotary deflector 5 deflects the laser beamsfrom the laser array 1 by one of the reflection surfaces. The focusingoptical system 6A focuses the deflected laser beams from the rotarydeflector 5 onto the scanned surface 9 to form the beam spots thereon.

[0101] Further, the light source device of the present embodiment foruse in the multi-beam scanning device according to the aboveconfiguration, includes the semiconductor laser array 1, the couplinglens 2 and the aperture stop 3, wherein the aperture stop is configuredto have a numerical aperture NAzS in the sub-scanning direction thatsatisfies the conditions:

0.01<NAzS<0.30  (3)

[0102] Next, a description will be given of first through sixthpreferred embodiments of the multi-beam scanning device of the inventionwith reference to the accompanying drawings FIG. 4 through FIG. 15B.

[0103] In some of the following preferred embodiments, one or aplurality of lenses having a non-spherical configuration may be providedin the focusing optical system 6A. First, a description will be providedof the non-spherical configuration of such lenses. However, the presentinvention is not limited to the non-spherical configuration of suchlenses, which will be described below.

[0104] A non-circular configuration of a lens of the focusing opticalsystem 6A, which is taken along a main-scanning cross-section (which isa flat cross-sectional plane containing the optical axis and beingparallel to the main scanning direction), is expressed as follows.

[0105] Suppose that “X” indicates a depth in the optical axis direction,“Y” indicates a coordinate in the main scanning direction, “Rm”indicates a radius of a paraxial curvature within the main-scanningcross-section, and “Km” and “Ai” (i=1, 2, 3, . . .) indicatemain-scanning coefficients. The depth X in the optical axis direction isrepresented by the following equation:

X=(Y²/R_(m))/[1+{square root}{square root over ()}{(1+K_(m))(Y/R_(m))²}]+ΣA_(i)Y^(i)  (10)

[0106] When a curvature within a sub-scanning cross-section (is a flatcross-sectional plane perpendicular to the main scanning direction) isvaried depending on the coordinate Y within the sub-scanningcross-section in the main scanning direction, the curvature Cs(Y) isrepresented by the following equation:

C_(s)(Y)={1/R_(s)(0)}+ΣB_(i)Y^(i)  (11)

[0107] where “R_(s)(0)” indicates a radius of a paraxial curvaturewithin the sub-scanning cross-section at Y=0, “Bi” indicatessub-scanning coefficients, and “i” indicates an integer (i=1, 2, 3, . .. ).

[0108] Next, the expression of a non-circular configuration of a lens ofthe focusing optical system 6A will be considered for a case in whichthe configuration of the lens within the main-scanning cross-section isnon-circular, the configuration of the lens within the sub-scanningcross-section is non-circular, and the non-circular configuration of thelens within the sub-scanning cross-section is varied depending on thecoordinate “Y” in the main-scanning direction. Suppose that “Z”indicates a coordinate in the sub-scanning direction. The depth X in theoptical axis direction in this case is represented by the followingequation: $\begin{matrix}\begin{matrix}{X = \quad {{\left( {Y^{2}/R_{m}} \right)/\left\lbrack {1 + \sqrt{\left\{ {\left( {1 + K_{m}} \right)\left( {Y/R_{m}} \right)^{2}} \right\}}} \right\rbrack} +}} \\{\quad {{\sum\quad {A_{i}Y^{i}}} +}} \\{\quad {{{C_{s}(Y)} \cdot {Z^{2}/\left\lbrack {1 + \sqrt{\left\{ {\left( {1 + K_{s}} \right)\left( {{C_{s}(Y)} \cdot Z} \right)^{2}} \right\}}} \right\rbrack}} +}} \\{\quad {{\left( {F_{o} + {F_{1} \cdot Y} + {F_{2} \cdot Y^{2}} + {F_{3} \cdot Y^{3}} + {F_{4} \cdot Y^{4}} + \cdots} \right) \cdot Z} +}} \\{\quad {{\left( {G_{o} + {G_{1} \cdot Y} + {G_{2} \cdot Y^{2}} + {G_{3} \cdot Y^{3}} + {G_{4} \cdot Y^{4}} + \cdots} \right) \cdot Z^{2}} +}} \\{\quad {{\left( {H_{o} + {H_{1} \cdot Y} + {H_{2} \cdot Y^{2}} + {H_{3} \cdot Y^{3}} + {H_{4} \cdot Y^{4}} + \cdots} \right) \cdot Z^{3}} +}} \\{\quad {{\left( {I_{o} + {I_{1} \cdot Y} + {I_{2} \cdot Y^{2}} + {I_{3} \cdot Y^{3}} + {I_{4} \cdot Y^{4}} + \cdots} \right) \cdot Z^{4}} +}} \\{\quad {{\left( {J_{o} + {J_{1} \cdot Y} + {J_{2} \cdot Y^{2}} + {J_{3} \cdot Y^{3}} + {J_{4} \cdot Y^{4}} + \cdots} \right) \cdot Z^{5}} +}} \\{\quad {{\left( {K_{o} + {K_{1} \cdot Y} + {K_{2} \cdot Y^{2}} + {K_{3} \cdot Y^{3}} + {K_{4} \cdot Y^{4}} + \cdots} \right) \cdot Z^{6}} +}} \\{\quad {{\left( {L_{o} + {L_{1} \cdot Y} + {L_{2} \cdot Y^{2}} + {L_{3} \cdot Y^{3}} + {L_{4} \cdot Y^{4}} + \cdots} \right) \cdot Z^{7}} +}} \\{\quad {{\left( {M_{o} + {M_{1} \cdot Y} + {M_{2} \cdot Y^{2}} + {M_{3} \cdot Y^{3}} + {M_{4} \cdot Y^{4}} + \cdots} \right) \cdot Z^{8}} +}} \\{\quad {{\left( {N_{o} + {N_{1} \cdot Y} + {N_{2} \cdot Y^{2}} + {N_{3} \cdot Y^{3}} + {N_{4} \cdot Y^{4}} + \cdots} \right) \cdot Z^{9}} +}} \\{\quad \cdots}\end{matrix} & (12)\end{matrix}$

[0109] where the coefficient “Ks” included in the third term of theequation (12) is represented by the equation

Ks(Y)=Ks(0)+Ci Y^(i)  (13)

[0110] where “Ks(0)” indicates a conical coefficient within thesub-scanning cross-section at Y=0, “Ci” indicates sub-scanningcoefficients, and “i” indicates an integer (i=1, 2, 3, . . . ).

[0111]FIG. 4 shows a configuration of the optical systems of a firstpreferred embodiment of the multi-beam scanning device.

[0112] As shown in FIG. 4, the multi-beam scanning device of thisembodiment generally comprises a semiconductor laser array 111, acoupling lens 121, an aperture stop 131, a cylindrical lens 141, arotary polygonal mirror 151, lenses 161, 171 and 181 of the focusingoptical system, and a scanned surface 19 of the photosensitive medium.

[0113] It is a matter of course that a planer mirror may be provided atan intermediate portion of the optical path between the light source 111and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

[0114] In the configuration of FIG. 4, the semiconductor laser array 111is provided with four light emitting parts, the array pitch ρ of thelight emitting parts ρ=14 μm, the emitted laser beam wavelength 780 nm,the maximum output power 15 mW, and the inclination angle φ=0 degrees.

[0115] The coupling lens 121 is provided with a one-group, two-lensconfiguration, the focal length 30 mm, and the collimating function.

[0116] The cylindrical lens 141 is provided with the focal length 70.62mm in the sub-scanning direction.

[0117] The aperture stop 131 is provided with the aperture width 5.2 mmin the main scanning direction and the aperture width 1.04 mm in thesub-scanning direction.

[0118] The rotary polygonal mirror 151 is provided with six reflectionsurfaces, the inscribed circle radius 25 mm, the incident angle (betweenthe laser beam incident direction of the light source and the opticalaxis of the focusing optical system) 60 degrees, the writing density1200 dpi, and the target beam spot diameter 50 μm.

[0119] The lenses 161, 171 and 181 of the focusing optical system areconfigured as in the following table. Suppose that “Rmi” indicates theradius of curvature of the i-th surface (counted from the side of therotary polygonal mirror) within the main-scanning cross-section, “Rsi”indicates the radius of curvature of the i-th surface within thesub-scanning cross-section, “X” indicates the distance between thesurfaces, “Y” indicates the shift amount of the surface in the upwarddirection in the plane of the shown configuration, and “n” indicates therefractive index. In the case of a lens having a non-circularconfiguration, the radius “Rmi” and the radius “Rsi” indicates theradius of the paraxial curvature of the i-th surface of suchconfiguration. The notation of the following table is applied to otherpreferred embodiments which will be described later. i Rmi Rsi X Y nMirror Surface 0 ∞ ∞ 51.38 1.627 Lens 161 1 −96.76 spherical 15.07 01.78571 2 −93.27 spherical 9.76 0 Lens 171 3 −2450.2 spherical 19.90 01.60909 4 −161.76 spherical 127.0 0 Lens 181 5 −630.00 −55.53 3.00 01.57211 6 −700.00 −24.42 101.72 0

[0120] The incident-side surface of the lens 181 (with the surfacenumber i=5) has the main-scanning cross-section in the non-circularconfiguration. The non-circular configuration of this surface takenalong the main-scanning cross-section is represented by the aboveequation (10). The following TABLE 1 provides the values of themain-scanning coefficients of the equation (10). TABLE 1 Surface No.Main-Scanning Coefficients 5 K  31.405 A₄  −2.059 × 10⁻⁹  A₆   1.839 ×10⁻¹⁴ A₈   6.366 × 10⁻¹⁸ A₁₀ −8.922 × 10⁻²² A₁₂  6.466 × 10⁻²⁶ A₁₄−1.339 × 10⁻³⁰ A₁₆ −1.058 × 10⁻³⁴ A₁₈  4.413 × 10⁻³⁹

[0121] In the first preferred embodiment, the multi-beam scanning deviceis configured to have the parameter K which is given by

[0122] K=0.82×780×10⁻³/50=0.01279.

[0123] The configuration of this embodiment meets the conditions of theabove formula (5). In the first preferred embodiment, the multi-beamscanning device is configured to have the parameter K·P/(ρ·cos φ) whichis given by

[0124] K·P/(ρ·cos φ)=0.01279×21.167/14=0.01934.

[0125] The configuration of this embodiment meets the conditions of theabove formula (9).

[0126]FIG. 5A and FIG. 5B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 4.

[0127] In the first preferred embodiment, the light emitting part “ch1”of the semiconductor laser array is positioned 21 μm apart from theoptical axis of the coupling lens 121 in the sub-scanning direction.With respect to the defocus amount of the beam spot (which is formed onthe scanned surface by the laser beam emitted from the light emittingpart “ch1”) at image-height positions of nine equal subdivisions of ±150mm, the relationship between the defocus amount and the beam spotdiameter in the main scanning direction is shown in FIG. 5A. Similarly,the relationship between the defocus amount and the beam spot diameterin the sub-scanning direction is shown in FIG. 5B.

[0128] As shown in FIG. 5A, the depth clearance in the main scanningdirection is 3.10 mm. As shown in FIG. 5B, the depth clearance in thesub-scanning direction is 2.25 mm. As both the depth clearances of thisembodiment are larger than 0.9 mm (based on the practical experience),the multi-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 1200 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

[0129] The numerical aperture NAzS of this embodiment is 0.01934. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of4.4 mJ/m² is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 11.44 mW. As the maximum output power of the laser array in thisembodiment is 15 mW, the insufficient light energy as in theconventional multi-beam scanning device does not occur for the presentembodiment.

[0130] Next, FIG. 6 shows a configuration of the optical systems of asecond preferred embodiment of the multi-beam scanning device.

[0131] As shown in FIG. 6, the multi-beam scanning device of thisembodiment generally comprises a semiconductor laser array 112, acoupling lens 122, an aperture stop 132, a cylindrical lens 142, arotary polygonal mirror 152, lenses 162 and 172 of the focusing opticalsystem, and the scanned surface 19 of the photosensitive medium.

[0132] It is a matter of course that a planer mirror may be provided atan intermediate portion of the optical path between the light source 112and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

[0133] In the configuration of FIG. 6, the semiconductor laser array 112is provided with four light emitting parts, the array pitch ρ of thelight emitting parts ρ=20 μm, the emitted laser beam wavelength 670 nm,the maximum output power 8 mW, and the inclination angle φ=29.45degrees.

[0134] The coupling lens 122 is provided with a single lensconfiguration, the focal length 30 mm, and the collimating function.

[0135] The cylindrical lens 142 is provided with the focal length 51.88mm in the sub-scanning direction.

[0136] The aperture stop 132 is provided with the aperture width 7.9 mmin the main scanning direction and the aperture width 1.2 mm in thesub-scanning direction.

[0137] The rotary polygonal mirror 152 is provided with five reflectionsurfaces, the inscribed circle radius 18 mm, the incident angle (betweenthe laser beam incident direction of the light source and the opticalaxis of the focusing optical system) 60 degrees, the writing density1200 dpi, and the target beam spot diameter 30 μm.

[0138] The lenses 162 and 172 of the focusing optical system areconfigured as in the following table. i Rmi Rsi X Y n Mirror Surface 0 ∞∞ 72.49 0.206 Lens 162 1 1617.54 −52.00 35.00 0 1.52657 2 −146.53−195.27 62.91 0.204 Lens 172 3 413.68 −71.31 13.94 0 1.52657 4 824.88−27.70 160.22 0

[0139] The surfaces (the surface number i=1, 2, 3) of the lenses 162 and172 have the non-circular configuration represented by the aboveequations (10) and (11). The surface (the surface number i=4) of thelens 172 has the non-circular configuration represented by the aboveequations (11) through (13). The following TABLE 2 through TABLE 6provide the values of the main-scanning coefficients and thesub-scanning coefficients of the equations (10) through (13)). TABLE 2Surface Main-Scanning Sub-Scanning Number Coefficients Coefficients 1 K 185  B₁ −1.069 × 10⁻⁵  A₁ 0 B₂ 2.323 × 10⁻⁶ A₂ 0 B₃ 2.768 × 10⁻⁹ A₃ 0 B₄−2.010 × 10⁻¹⁰ A₄ 1.284 × 10⁻⁸ B₅ −5.286 × 10⁻¹³ A₅ 0 B₆  1.603 × 10⁻¹⁴A₆ −6.017 × 10⁻¹³ B₇  4.005 × 10⁻¹⁷ A₇ 0 B₈ −5.616 × 10⁻¹⁹ A₈ −8.040 ×10⁻¹⁷ B₉  1.444 × 10⁻²⁰ A₉ 0  B₁₀  1.834 × 10⁻²¹  A₁₀  5.138 × 10⁻²¹ B₁₁ −2.465 × 10⁻²⁴  A₁₁ 0  B₁₂  1.419 × 10⁻²⁵

[0140] TABLE 3 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 2 K  −1.934 × 10⁻¹  B₁ 0 A₁ 0 B₂ −2.116 × 10⁻⁶  A₂ 0 B₃ 0A₃ 0 B₄  4.472 × 10⁻¹¹ A₄ 1.790 × 10⁻⁸ B₅ 0 A₅ 0 B₆  3.322 × 10⁻¹⁴ A₆ 2.847 × 10⁻¹³ B₇ 0 A₇ 0 B₈ −1.366 × 10⁻¹⁸ A₈ −3.723 × 10⁻¹⁷ B₉ 0 A₉ 0 B₁₀ −6.548 × 10⁻²²  A₁₀  5.930 × 10⁻²¹  B₁₁ 0  A₁₁ 0  B₁₂ −4.619 ×10⁻²⁶

[0141] TABLE 4 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 3 K  −13.95 B₁ 0 A₁ 0 B₂ −1.958 × 10⁻⁷  A₂ 0 B₃ 0 A₃ 0 B₄ 2.316 × 10⁻¹¹ A₄ −6.790 × 10⁻⁹  B₅ 0 A₅ 0 B₆ −1.140 × 10⁻¹⁵ A₆ −2.046 ×10⁻¹³ B₇ 0 A₇ 0 B₈  1.179 × 10⁻²⁰ A₈  7.466 × 10⁻¹⁸ B₉ 0 A₉ 0  B₁₀ 9.187 × 10⁻²⁵  A₁₀  5.282 × 10⁻²²  B₁₁ 0  A₁₁ 0  B₁₂ −5.552 × 10⁻²⁹ A₁₂ −8.143 × 10⁻²⁷  B₁₃ 0  A₁₃ 0  B₁₄ 0  A₁₄ −3.771 × 10⁻³³  B₁₅ 0

[0142] TABLE 5 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 4 K  −69.07 B₁ −9.030 × 10⁻⁷  A₁ 0 B₂ 4.204 × 10⁻⁷ A₂ 0 B₃−2.211 × 10⁻¹¹ A₃ 0 B₄ −3.115 × 10⁻¹¹ A₄ −1.348 × 10⁻⁸ B₅  1.857 × 10⁻¹⁵A₅ 0 B₆  1.289 × 10⁻¹⁵ A₆  8.953 × 10⁻¹⁴ B₇ −1.444 × 10⁻¹⁹ A₇ 0 B₈ 3.211 × 10⁻²¹ A₈  1.936 × 10⁻¹⁷ B₉  2.173 × 10⁻²³ A₉ 0  B₁₀ −9.827 ×10⁻²⁵  A₁₀ −2.840 × 10⁻²²  B₁₁ −9.598 × 10⁻²⁸  A₁₁ 0  B₁₂ −1.663 × 10⁻²⁹ A₁₂  6.044 × 10⁻²⁷  B₁₃ 0  A₁₃ 0  B₁₄ 0  A₁₄  1.077 × 10⁻³¹  B₁₅ 0

[0143] TABLE 6 4 C₀ −1.000 I₀ −8.009 × 10⁻⁷  K₀ −1.179 × 10⁻⁹  C₁ 0 I₁−8.846 × 10⁻¹¹ K₁ −9.850 × 10⁻¹³ C₂ 0 1₂  7.158 × 10⁻¹¹ K₂ −9.672 ×10⁻¹⁴ C₃ 0 1₃ −1.870 × 10⁻¹³ K₃  1.828 × 10⁻¹⁵ C₄ 0 1₄ −2.617 × 10⁻¹⁴ K₄ 1.860 × 10⁻¹⁶ C₅ 0 I₅  6.722 × 10⁻¹⁷ K₅ −6.285 × 10⁻¹⁹ C₆ 0 I₆  5.872 ×10⁻¹⁸ K₆ −5.428 × 10⁻²⁰ C₇ 0 I₇ −9.322 × 10⁻²¹ K₇  8.632 × 10⁻²³ C₈ 0 I₈−6.141 × 10⁻²² K₈  6.187 × 10⁻²⁴ C₉ 0 I₉  5.471 × 10⁻²⁵ K₉ −5.030 ×10⁻²⁷  C₁₀ 0  I₁₀  2.868 × 10⁻²⁶  K₁₀ −3.015 × 10⁻²⁸  C₁₁ 0  I₁₁ −1.116× 10⁻²⁹  K₁₁  1.019 × 10⁻³¹  C₁₂ 0  I₁₂ −4.938 × 10⁻³¹  K₁₂  5.340 ×10⁻³³

[0144] In the second preferred embodiment, the multi-beam scanningdevice is configured to have the parameter K which is given by

[0145] K=0.82×670×10⁻³/30=0.01831.

[0146] The configuration of this embodiment meets the conditions of theabove formula (5). In the second preferred embodiment, the multi-beamscanning device is configured to have the parameter K·P/(ρ·cos φ) whichis given by

[0147] K·P/(ρ·cos φ)=0.01831×21.167/20·cos (29.45 deg.)=0.02225.

[0148] The configuration of this embodiment meets the conditions of theabove formula (9).

[0149]FIG. 7A and FIG. 7B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 6.

[0150] In the second preferred embodiment, the light emitting part “ch1”of the semiconductor laser array is positioned 28.43 μm apart from theoptical axis of the coupling lens 122 in the sub-scanning direction.With respect to the defocus amount of the beam spot (which is formed onthe scanned surface by the laser beam emitted from the light emittingpart “ch1” ) at image-height positions of twenty-one equal subdivisionsof ±150 mm, the relationship between the defocus amount and the beamspot diameter in the main scanning direction is shown in FIG. 7A.Similarly, the relationship between the defocus amount and the beam spotdiameter in the sub-scanning direction is shown in FIG. 7B.

[0151] As shown in FIG. 7A, the depth clearance in the main scanningdirection is 1.57 mm. As shown in FIG. 7B, the depth clearance in thesub-scanning direction is 2.00 mm. As both the depth clearances of thisembodiment are larger than 0.9 mm (based on the practical experience),the multi-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 1200 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

[0152] The numerical aperture NAzS of this embodiment is 0.02225. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of6.3 mJ/m² is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 7.22 mW. As the maximum output power of the laser array in thisembodiment is 8 mW, the insufficient light energy as in the conventionalmulti-beam scanning device does not occur for the present embodiment.

[0153] Next, FIG. 8 shows a configuration of the optical systems of athird preferred embodiment of the multi-beam scanning device.

[0154] As shown in FIG. 8, the multi-beam scanning device of thisembodiment generally comprises a semiconductor laser array 113, acoupling lens 123, an aperture stop 133, a cylindrical lens 143, arotary polygonal mirror 153, lenses 163, 173 and 183 of the focusingoptical system, and the scanned surface 19 of the photosensitive medium.

[0155] It is a matter of course that a planer mirror may be provided atan intermediate portion of the optical path between the light source 113and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

[0156] In the configuration of FIG. 8, the semiconductor laser array 113is provided with four light emitting parts, the array pitch ρ of thelight emitting parts ρ=14 μm, the emitted laser beam wavelength 780 nm,the maximum output power 10 mW, and the inclination angle φ=0 degrees.

[0157] The coupling lens 123 is provided with a single lensconfiguration, the focal length 15 mm, and the collimating function.

[0158] The cylindrical lens 143 is provided with the focal length 70.62mm in the sub-scanning direction.

[0159] The aperture stop 133 is provided with the aperture width 5.5 mmin the main scanning direction and the aperture width 0.88 mm in thesub-scanning direction.

[0160] The rotary polygonal mirror 153 is provided with six reflectionsurfaces, the inscribed circle radius 25 mm, the incident angle (betweenthe laser beam incident direction of the light source and the opticalaxis of the focusing optical system) 60 degrees, the writing density 600dpi, and the target beam spot diameter 60 μm.

[0161] The lenses 163, 173 and 183 of the focusing optical system areconfigured as in the following table. i Rmi Rsi X Y n Mirror Surface 0 ∞∞ 51.38 1.627 Lens 163 1 −96.76 spherical 15.07 0 1.78571 2 −93.27spherical 9.76 0 Lens 173 3 −2450.2 spherical 19.90 0 1.60909 4 −161.76spherical 127.0 0 Lens 183 5 −630.00 −55.53 3.00 0 1.57211 6 −700.00−24.42 101.72 0

[0162] The incident-side surface of the lens 183 (with the surfacenumber i=5) has the main-scanning cross-section in the non-circularconfiguration. The non-circular configuration of this surface takenalong the main-scanning cross-section is represented by the aboveequation (10). The following TABLE 7 provides the values of themain-scanning coefficients of the equation (10). TABLE 7 Surface No.Main-Scanning Coefficients 5 K −31.405 A₄  −2.059 × 10⁻⁹  A₆   1.839 ×10⁻¹⁴ A₈   6.366 × 10⁻¹⁸ A₁₀ −8.922 × 10⁻²² A₁₂  6.466 × 10⁻²⁶ A₁₄−1.339 × 10⁻³⁰ A₁₆ −1.058 × 10⁻³⁴ A₁₈  4.413 × 10⁻³⁹

[0163] The focusing optical system of the third preferred embodiment isthe same as that of the first preferred embodiment. In the thirdpreferred embodiment, the multi-beam scanning device is configured tohave the parameter K which is given by

[0164] K=0.82×780×10⁻³/60=0.01066.

[0165] The configuration of this embodiment meets the conditions of theabove formula (5). In the third preferred embodiment, the multi-beamscanning device is configured to have the parameter K·P (ρ·cos φ) whichis given by

[0166] K·P/(ρ·cos φ)=0.01066×42.333/14=0.03223.

[0167] The configuration of this embodiment meets the conditions of theabove formula (9).

[0168]FIG. 9A and FIG. 9B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 8.

[0169] In the third preferred embodiment, the light emitting part “ch1”of the semiconductor laser array is positioned 21 μm apart from theoptical axis of the coupling lens 123 in the sub-scanning direction.With respect to the defocus amount of the beam spot (which is formed onthe scanned surface by the laser beam emitted from the light emittingpart “ch1”) at image-height positions of nine equal subdivisions of ±150mm, the relationship between the defocus amount and the beam spotdiameter in the main scanning direction is shown in FIG. 9A. Similarly,the relationship between the defocus amount and the beam spot diameterin the sub-scanning direction is shown in FIG. 9B.

[0170] As shown in FIG. 9A, the depth clearance in the main scanningdirection is 8.10 mm. As shown in FIG. 9B, the depth clearance in thesub-scanning direction is 4.51 mm. As both the depth clearances of thisembodiment are larger than 0.9 mm (based on the practical experience),the multi-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 600 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

[0171] The numerical aperture NAzS of this embodiment is 0.03223. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of6.3 mJ/m² is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 7.28 mW. As the maximum output power of the laser array in thisembodiment is 10 mW, the insufficient light energy as in theconventional multi-beam scanning device does not occur for the presentembodiment.

[0172] Next, FIG. 10 shows a configuration of the optical systems of afourth preferred embodiment of the multi-beam scanning device.

[0173] As shown in FIG. 10, the multi-beam scanning device of thisembodiment generally comprises a semiconductor laser array 114, acoupling lens 124, an aperture stop 134, a cylindrical lens 144, arotary polygonal mirror 154, lenses 164 and 174 of the focusing opticalsystem, and the scanned surface 19 of the photosensitive medium.

[0174] It is a matter of course that a planer mirror may be provided atan intermediate portion of the optical path between the light source 114and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

[0175] In the configuration of FIG. 10, the semiconductor laser array114 is provided with four light emitting parts, the array pitch ρ of thelight emitting parts ρ=14 μm, the emitted laser beam wavelength 780 nm,the maximum output power 10 mW, and the inclination angle φ=62.3degrees.

[0176] The coupling lens 124 is provided with a single lensconfiguration, the focal length 27 mm, and the collimating function.

[0177] The cylindrical lens 144 is provided with the focal length 126.18mm in the sub-scanning direction.

[0178] The aperture stop 134 is provided with the aperture width 6.56 mmin the main scanning direction and the aperture width 2.3 mm in thesub-scanning direction.

[0179] The rotary polygonal mirror 154 is provided with five reflectionsurfaces, the inscribed circle radius 18 mm, the incident angle (betweenthe laser beam incident direction of the light source and the opticalaxis of the focusing optical system) 60 degrees, the writing density1200 dpi, and the target beam spot diameter 45,μm.

[0180] The lenses 164 and 174 of the focusing optical system areconfigured as in the following table. i Rmi Rsi X Y n Mirror Surface 0 ∞∞ 72.56 0.286 Lens 164 1 1616.43 −50.14 35.00 0 1.52398 2 −146.51−199.81 61.93 0.254 Lens 174 3 400.87 −72.03 14.00 0 1.52398 4 824.88−27.59 160.56 0

[0181] The surfaces (the surface number i=1, 2, 3) of the lenses 164 and174 have the non-circular configuration represented by the aboveequations (10) and (11). The surface (the surface number i=4) of thelens 174 has the non-circular configuration represented by the aboveequations (11) through (13). The following TABLE 8 through TABLE 12provide the values of the main-scanning coefficients and thesub-scanning coefficients of the equations (10) through (13). TABLE 8Surface Main-Scanning Sub-Scanning Number Coefficients Coefficients 1 K1.976 × 10⁺² B₁ −1.162 × 10⁻⁵  A₁ 0 B₂ 2.276 × 10⁻⁶ A₂ 0 B₃ 2.714 × 10⁻⁹A₃ 0 B₄ −1.544 × 10⁻¹⁰ A₄ 1.281 × 10⁻⁸ B₅ −4.265 × 10⁻¹³ A₅ 0 B₆  6.417× 10⁻¹⁵ A₆ −6.374 × 10⁻¹³ B₇  9.179 × 10⁻¹⁹ A₇ 0 B₈ −1.230 × 10⁻¹⁹ A₈−9.428 × 10⁻¹⁷ B₉  1.453 × 10⁻²⁰ A₉ 0  B₁₀ −1.881 × 10⁻²²  A₁₀  5.965 ×10⁻²¹  B₁₁ −1.468 × 10⁻²⁴  A₁₁ 0  B₁₂ −2.670 × 10⁻²⁶

[0182] TABLE 9 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 2 K −1.857 × 10⁻¹  B₁ 0 A₁ 0 B₂ −2.125 × 10⁻⁶  A₂ 0 B₃ 0 A₃0 B₄ 1.805 × 10⁻¹¹ A₄ 1.774 × 10⁻⁸  B₅ 0 A₅ 0 B₈ 2.716 × 10⁻¹⁴ A₆ 1.384× 10⁻¹³ B₇ 0 A₇ 0 B₈ 6.924 × 10⁻¹⁹ A₈ −4.354 × 10⁻¹⁷  B₉ 0 A₉ 0  B₁₀−2.685 × 10⁻²²   A₁₀ 7.168 × 10⁻²¹  B₁₁ 0  A₁₁ 0  B₁₂ −5.778 × 10⁻²⁶ 

[0183] TABLE 10 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 3 K −12.60 B₁ 0 A₁ 0 B₂ −1.962 × 10⁻⁷  A₂ 0 B₃ 0 A₃ 0 B₄2.230 × 10⁻¹¹ A₄ −7.349 × 10⁻⁹  B₅ 0 A₅ 0 B₆ −1.022 × 10⁻¹⁵  A₆ −2.106 ×10⁻¹³ B₇ 0 A₇ 0 B₈ 1.081 × 10⁻²⁰ A₈  8.173 × 10⁻¹⁸ B₉ 0 A₉ 0  B₁₀ 6.363× 10⁻²⁵  A₁₀  5.409 × 10⁻²²  B₁₁ 0  A₁₁ 0  B₁₂ −3.645 × 10⁻²⁹   A₁₂−1.082 × 10⁻²⁶  B₁₃ 0  A₁₃ 0  B₁₄ 0  A₁₄ −2.039 × 10⁻³²  B₁₅ 0

[0184] TABLE 11 Surface Main-Scanning Sub-Scanning Number CoefficientsCoefficients 4 K −71.068 B₁ −8.546 × 10⁻⁷  A₁ 0 B₂ 4.161 × 10⁻⁷ A₂ 0 B₃−2.523 × 10⁻¹¹ A₃ 0 B₄ −2.960 × 10⁻¹¹ A₄ −1.324 × 10⁻⁸  B₅  2.114 ×10⁻¹⁶ A₅ 0 B₆  1.160 × 10⁻¹⁵ A₆ 9.662 × 10⁻¹⁴ B₇  4.372 × 10⁻²² A₇ 0 B₈−1.098 × 10⁻²¹ A₈ 1.888 × 10⁻¹⁷ B₉  5.560 × 10⁻²⁴ A₉ 0  B₁₀ −7.785 ×10⁻²⁵  A₁₀ −3.102 × 10⁻²²   B₁₁ −1.617 × 10⁻²⁹  A₁₁ 0  B₁₂  3.262 ×10⁻³⁰  A₁₂ 7.298 × 10⁻²⁷  B₁₃ 0  A₁₃ 0  B₁₄ 0  A₁₄ 2.305 × 10⁻³²  B₁₅ 0

[0185] TABLE 12 4 C₀ −3.940 ×  I₀ 2.869 × K₀ −1.526 × 10⁻¹  10⁻⁶  10⁻⁹ C₁ 1.796 × I₁ 4.012 × K₁ −3.101 × 10⁻⁴  10⁻¹¹ 10⁻¹¹ C₂ 2.425 × I₂ 1.690× K₂ −8.903 × 10⁻⁶  10⁻¹¹ 10⁻¹² C₃ 4.438 × I₃ 3.572 × K₃  5.017 × 10⁻⁸ 10⁻¹⁴ 10⁻¹⁴ C₄ 4.584 × I₄ −8.742 ×  K₄  3.241 × 10⁻¹⁰ 10⁻¹⁵ 10⁻¹⁵ C₅−2.438 ×  I₅ 1.964 × K₅ −7.703 × 10⁻¹² 10⁻¹⁸ 10⁻¹⁸ C₆ −3.396 ×  I₆ 8.603× K₆ −4.104 × 10⁻¹⁴ 10⁻¹⁹ 10⁻¹⁹ C₇ 4.132 × I₇ 6.160 × K₇  5.118 × 10⁻¹⁷10⁻²³ 10⁻²² C₈ 6.805 × I₈ −3.347 ×  K₈  2.368 × 10⁻¹⁹ 10⁻²³ 10⁻²³ C₉ 0I₉ −3.693 ×  K₉ −1.550 × 10⁻²⁸ 10⁻²⁶  C₁₀ 0  I₁₀ 4.536 ×  K₁₀ −6.371 ×10⁻²⁸ 10⁻²⁸  C₁₁ 0  I₁₁ 0  K₁₁  1.748 × 10⁻³¹  C₁₂ 0  I₁₂ 0  K₁₂  6.503× 10⁻³³

[0186] In the fourth preferred embodiment, the multi-beam scanning 5device is configured to have the parameter K which is given by

[0187] K=0.82×780×10⁻³/45=0.01421.

[0188] The configuration of this embodiment meets the conditions of theabove formula (5). In the fourth preferred embodiment, the multi-beamscanning device is configured to have the parameter K·P/(ρ·cos φ) whichis given by

[0189] K·P/(ρ·cos φ)=0.01421×21.167/14·cos (62.3 deg.)=0.04622.

[0190] The configuration of this embodiment meets the conditions of theabove formula (9).

[0191]FIG. 11A and FIG. 11B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 10.

[0192] In the fourth preferred embodiment, the light emitting part “ch1”of the semiconductor laser array is positioned 18.48,μm apart from theoptical axis of the coupling lens 124 in the sub-scanning direction.With respect to the defocus amount of the beam spot (which is formed onthe scanned surface by the laser beam emitted from the light emittingpart “ch1”) at image-height positions of nine equal subdivisions of ±150mm, the relationship between the defocus amount and the beam spotdiameter in the main scanning direction is shown in FIG. 11A. Similarly,the relationship between the defocus amount and the beam spot diameterin the sub-scanning direction is shown in FIG. 11B.

[0193] As shown in FIG. 11A, the depth clearance in the main scanningdirection is 3.04 mm. As shown in FIG. 11B, the depth clearance in thesub-scanning direction is 3.93 mm. As both the depth clearances of thisembodiment are larger than 0.9 mm (based on the practical experience),the multi-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 1200 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

[0194] The numerical aperture NAzS of this embodiment is 0.04622. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of6.3 mJ/m² is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 7.40 mW. As the maximum output power of the laser array in thisembodiment is 10 mW, the insufficient light energy as in theconventional multi-beam scanning device does not occur for the presentembodiment.

[0195] Next, FIG. 12A and FIG. 12B show a configuration of the opticalsystems of a fifth preferred embodiment of the multi-beam scanningdevice. The configuration of this embodiment in the main scanningdirection is shown in FIG. 12A, and the configuration of this embodimentin the sub-scanning direction is shown in FIG. 12B.

[0196] As shown in FIG. 12A and FIG. 12B, the multi-beam scanning deviceof this embodiment generally comprises a semiconductor laser array 115,a coupling lens 125, an aperture stop 135, a cylindrical lens 145, arotary polygonal mirror 155, three lenses 165, 175 and 185 and acylindrical mirror 18M of the focusing optical system, and the scannedsurface 19 of the photosensitive medium.

[0197] It is a matter of course that a planer mirror may be provided atan intermediate portion of the optical path between the light source 115and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

[0198] In the configuration of FIG. 12A and FIG. 12B, the semiconductorlaser array 115 is provided with four light emitting parts, the arraypitch ρ of the light emitting parts ρ=10 μm, the emitted laser beamwavelength 670 nm, the maximum output power 8 mW, and the inclinationangle φ=0 degrees.

[0199] The coupling lens 125 is provided with a two-group, three-lensconfiguration, the focal length 22 mm, and the collimating function.

[0200] The cylindrical lens 145 is provided with a two-lens combinedconfiguration and the focal length 189.77 mm in the sub-scanningdirection.

[0201] The aperture stop 135 is provided with the aperture width 10.5 mmin the main scanning direction and the aperture width 1.96 mm in thesub-scanning direction.

[0202] The rotary polygonal mirror 156 is provided with six reflectionsurfaces, the inscribed circle radius 65 mm, the incident angle 60degrees, the writing density 850 dpi, and the target beam spot diameter35 μm.

[0203] The lenses 165, 175, 185 and the mirror 18M of the focusingoptical system are configured as in the following table. i Rmi Rsi X Y nMirror Surface 0 ∞ ∞ 45.50 0.499 Lens 165 1 −78.22 spherical 9.80 01.58700 2 −1115.4 spherical 3.95 0 Lens 175 3 −318.06 spherical 20.6 01.78097 4 −112.85 spherical 2.04 0 Lens 185 5 639.11 spherical 23.00 01.45419 6 −158.15 spherical 315.00 0 Mirror 18M 7 ∞ −169.87 99.97 0

[0204] In the fifth preferred embodiment, the multi-beam scanning deviceis configured to have the parameter K which is given by

[0205] K=0.82×670×10⁻³/35=0.01570.

[0206] The configuration of this embodiment meets the conditions of theabove formula (5). In the third preferred embodiment, the multi-beamscanning device is configured to have the parameter K·P/(ρ·cos φ) whichis given by

[0207] K·P/(ρ·cos φ)=0.01570×29.882/10=0.04691.

[0208] The configuration of this embodiment meets the conditions of theabove formula (9).

[0209]FIG. 13A and FIG. 13B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 12A and FIG. 12B.

[0210] In the fifth preferred embodiment, the light emitting part “ch1”of the semiconductor laser array is positioned 15 μm apart from theoptical axis of the coupling lens 125 in the sub-scanning direction.With respect to the defocus amount of the beam spot (which is formed onthe scanned surface by the laser beam emitted from the light emittingpart “ch1”) at image-height positions of nine equal subdivisions of ±150mm, the relationship between the defocus amount and the beam spotdiameter in the main scanning direction is shown in FIG. 13A. Similarly,the relationship between the defocus amount and the beam spot diameterin the sub-scanning direction is shown in FIG. 13B.

[0211] As shown in FIG. 13A, the depth clearance in the main scanningdirection is 2.46 mm. As shown in FIG. 13B, the depth clearance in thesub-scanning direction is 2.58 mm. As both the depth clearances of thisembodiment are larger than 0.9 mm (based on the practical experience),the multi-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 850 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

[0212] The numerical aperture NAzS of this embodiment is 0.04691. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of5.5 mJ/m² is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 4.96 mW. As the maximum output power of the laser array in thisembodiment is 8 mW, the insufficient light energy as in the conventionalmulti-beam scanning device does not occur for the present embodiment.

[0213] Next, FIG. 14 shows a configuration of the optical systems of asixth preferred embodiment of the multi-beam scanning device.

[0214] As shown in FIG. 14, the multi-beam scanning device of thisembodiment generally comprises a semiconductor laser array 116, acoupling lens 126, an aperture stop 136, a beam expander BX, acylindrical lens 146, a rotary polygonal mirror 156, lenses 166, 176 and186 of the focusing optical system, and the scanned surface 19 of thephotosensitive medium.

[0215] It is a matter of course that a planer mirror may be provided atan intermediate portion of the optical path between the light source 116and the scanned surface 19 to bend the optical path in conformity withthe practical layout of the multi-beam scanning device.

[0216] In the configuration of FIG. 14, the semiconductor laser array116 is provided with four light emitting parts, the array pitch ρ of thelight emitting parts ρ=10 μm, the emitted laser beam wavelength 780 nm,the maximum output power 10 mW, and the inclination angle φ=81.14degrees.

[0217] The coupling lens 126 is provided with a two-group, three-lensconfiguration, the focal length 35 mm, and the coupling function toconvert the divergent laser beams emitted by the semiconductor laserarray into less divergent laser beams.

[0218] The beam expander BX is provided between the coupling lens andthe rotary deflector to enlarge the diameter of the laser beams, passedthrough the coupling lens, in the main scanning direction. The beamexpander BX does not provide any beam expanding function to enlarge thediameter of the laser beams in the sub-scanning direction. Themagnification factor of the beam expander BX is 10.

[0219] The cylindrical lens 146 is provided with the focal length 149.43mm in the sub-scanning direction.

[0220] The aperture stop 136 is provided with the aperture width 2.04 mmin the main scanning direction and the aperture width 17.4 mm in thesub-scanning direction.

[0221] The rotary polygonal mirror 156 is provided with eight reflectionsurfaces, the inscribed circle radius 75 mm, the incident angle (betweenthe laser beam incident direction of the light source and the opticalaxis of the focusing optical system) 50 degrees, the writing density1200 dpi, and the target beam spot diameter 35 μm.

[0222] The lenses 166, 176 and 186 of the focusing optical system areconfigured as in the following table. i Rmi Rsi X Y n Mirror Surface 0 ∞∞ 108.00 0.381 Lens 166 1 −126.00 spherical 13.10 0 1.58201 2 ∞ 142.9510.60 0 Lens 176 3 −2450.0 spherical 22.50 0 1.49282 4 −150.00 spherical5.60 0 Lens 186 5 ∞ ∞ 27.00 0 1.70400 6 −294.00 −81.10 655.10 0

[0223] In the sixth embodiment, the inclination angle φ is set to 81.14degrees that is near 90 degrees. The far-field pattern of thisembodiment is similar to that shown in FIG. 3D. The diameter of thelaser beams emitted from the laser array is small in the main scanningdirection and large in the sub-scanning direction. In order to obtain anadequate laser beam diameter needed for the main scanning direction, thecoupling function of the coupling lens 126 is insufficient. For thisreason, the beam expander BX is provided to enlarge the diameter of thelaser beams in the main scanning direction.

[0224] In the sixth preferred embodiment, the multi-beam scanning deviceis configured to have the parameter K which is given by

[0225] K=0.82×780×10⁻³/35=0.01827.

[0226] The configuration of this embodiment meets the conditions of theabove formula (5). In the third preferred embodiment, the multi-beamscanning device is configured to have the parameter K·P/(ρ·cos φ) whichis given by

[0227] K·P/(ρ·cos φ)=0.01827×21.167/1·cos (81.14 deg.)=0.25108.

[0228] The configuration of this embodiment meets the conditions of theabove formula (9).

[0229]FIG. 15A and FIG. 15B are diagrams for explaining the relationshipbetween the defocus amount and the spot diameter in the multi-beamscanning device of FIG. 14.

[0230] In the sixth preferred embodiment, the light emitting part “ch1”of the semiconductor laser array is positioned 12.57 μm apart from theoptical axis of the coupling lens 126 in the sub-scanning direction.With respect to the defocus amount of the beam spot (which is formed onthe scanned surface by the laser beam emitted from the light emittingpart “ch1”) at image-height positions of nine equal subdivisions of +150mm, the relationship between the defocus amount and the beam spotdiameter in the main scanning direction is shown in FIG. 15A. Similarly,the relationship between the defocus amount and the beam spot diameterin the sub-scanning direction is shown in FIG. 15B.

[0231] As shown in FIG. 15A, the depth clearance in the main scanningdirection is 2.22 mm. As shown in FIG. 15B, the depth clearance in thesub-scanning direction is 1.65 mm. As both the depth clearances of thisembodiment are larger than 0.9 mm (based on the practical experience),the multi-beam scanning device of this embodiment ensures adequate depthclearance even when the optical scanning is performed at the writingdensity of 1200 dpi, and effectively reduces the variations of the beamspots on the scanned surface to the small level so that the multi-beamscanning is carried out with accurate beam spot diameter.

[0232] The numerical aperture NAzS of this embodiment is 0.25108. It isconfirmed that the variations of the divergence angle for the respectivelight emitting parts of the semiconductor laser array are effectivelyreduced. When a photoconductive material having the exposure energy of4.4 mJ/m2 is used as the photosensitive medium in this embodiment, thethreshold level of the exposure energy at the scanning speed 380.8 m/secis 9.38 mW. As the maximum output power of the laser array in thisembodiment is 10 mW, the insufficient light energy as in theconventional multi-beam scanning device does not occur for the presentembodiment.

[0233] Finally, FIG. 16 shows a configuration of one preferredembodiment of the image forming apparatus of the present invention.

[0234] In the present embodiment, the image forming apparatus of theinvention is applied to a laser printer, and one embodiment of themulti-beam scanning device of the invention is provided in the laserprinter.

[0235] As shown in FIG. 16, the laser printer 1000 includes aphotoconductive drum 1110 which is provided as the photosensitive mediumthat is exposed to an imaging light pattern provided by the multi-beamscanning device. At surrounding portions around the photoconductive drum1110, a charging roller 1121, a developing unit 1131, a transfer roller1141, and a cleaning unit 1151 are provided. A known corona charger maybe used as the charging unit 1121.

[0236] In the laser printer 1000 of FIG. 16, a multi-beam scanningdevice 1171 according to one embodiment of the present invention isprovided, and a scanned surface of the photoconductive drum 1110, whichis located between the charging unit 1121 and the developing unit 1131,is exposed to multiple laser beams LB provided by the multi-beamscanning device 1171.

[0237] Further, in the laser printer 1000 of FIG. 16, a fixing unit1141, a paper cassette 1181, registration rollers 1191, a paper feedingroller 1201, a transport passage 1211, ejection rollers 1221, and apaper tray 1231 are provided. In the paper cassette 1181, a plurality ofcopy sheets P are contained.

[0238] When an image forming operation is performed by the laser printer1000, the photoconductive drum 1110 is rotated at a constant speed in aclockwise rotation direction as indicated by the arrow in FIG. 16. Thesurface of the photoconductive drum 1110 is uniformly charged by thecharging unit 1121. The charged surface of the photoconductive drum 1110is exposed to the multiple laser beams LB (the imaging light pattern)provided by the multi-beam scanning device 1171, so that anelectrostatic latent image is formed on the scanned surface of thephotoconductive drum 1110. In the present embodiment, the electrostaticlatent image is a negative latent image.

[0239] Further, the developing unit 1131 develops the latent image ofthe photoconductive drum 1110 with toner, and a toned image is producedon the scanned surface of the photoconductive drum 1110.

[0240] In the laser printer 1000, the paper cassette 1181 is removablyattached to the main body of the laser printer 1000 as shown in FIG. 16.One of the copy sheets P from the paper cassette 1181 is delivered tothe inside of the main body by the paper feeding roller 1201. Theleading end of this copy sheet is held between the registration rollers1191. At a timing that is synchronous to the time the toned image of thephotoconductive drum 1110 is moved to a transferring point, theregistration rollers 1191 deliver the copy sheet through the locationbetween the transferring roller 1141 and the photoconductive drum 1110.The transferring roller 1141 electrostatically transfers the toned imagefrom the photoconductive drum 1110 to the copy sheet that is deliveredby the registration rollers 1191.

[0241] The copy sheet, after the image transferring is performed, isdelivered to the fixing unit 1161. The fixing unit 1161 performs athermal fusing of the toner to the copy sheet. The copy sheet, after thethermal fusing is performed, is delivered through the transport passage1211 to the ejection rollers 1221. The ejection rollers 1221 deliversthe copy sheet to the tray 1231 which is provided outside the main bodyof the laser printer 1000. The cleaning unit 1151 performs a cleaning ofthe residual toner from the surface of the photoconductive drum 1110.

[0242] In the above-described laser printer 1000, OHP (overheadprojector) sheets may be used instead of the copy sheet P. Further, thetransferring of the toned image from the photoconductive drum 1110 tothe copy sheet may be performed by using an intermediate transferringmedium such as an intermediate transferring belt.

[0243] In the above-described laser printer 1000, the multi-beamscanning device 1171 according to the present invention can ensureadequate depth clearance when the optical scanning is performed at ahigh density. The multi-beam scanning device 1171 according to thepresent invention is effective in reducing the variations of the beamspots on the scanned surface, so that the multi-beam scanning is carriedout with accurate beam spot diameter so as to create good quality of areproduced image. Therefore, the laser printer 1000 in which themulti-beam scanning device 1171 of the present invention is provided cancreate good quality of a reproduced image.

[0244] The present invention is not limited to the above-describedembodiment, and variations and modifications may be made withoutdeparting from the scope of the present invention.

[0245] Further, the present invention is based on Japanese priorityapplication No.2000-044929, filed on Feb. 22, 2000, and Japanesepriority application No.2000-046368, filed on Feb. 23, 2000, the entirecontents of which are hereby incorporated by reference.

What is claimed is
 1. A multi-beam scanning device comprising: asemiconductor laser array having a plurality of light emitting partsemitting multiple laser beams; a rotary deflector deflecting the laserbeams emitted by the light emitting parts of the semiconductor laserarray; and a focusing optical system focusing the deflected laser beamsfrom the rotary deflector onto a scanned surface to form a plurality ofbeam spots that are separated on the scanned surface in a sub-scanningdirection, the scanned surface being scanned simultaneously with theplurality of beam spots in a main scanning direction by a rotation ofthe rotary deflector, wherein the laser array is configured such thatthe light emitting parts are arrayed along a line that is at aninclination angle φ to the sub-scanning direction, the inclination angleφ measured in degrees and meeting the conditions 0≦φ<90, and that ascanning line pitch P, an array pitch ρ of the light emitting parts ofthe laser array and a parameter K defined by the equation K=0.82 λ/ωz,where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions: 0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0.
 030. 2. The multi-beamscanning device of claim 1 further comprising: a coupling lens couplingthe laser beams emitted by the laser array; an aperture stop restrictinga diameter of the laser beams passed through the coupling lens; and aline focusing lens providing a refraction power to the laser beams,passed through the aperture stop, with respect to only the sub-scanningdirection, the rotary deflector having reflection surfaces, the rotarydeflector deflecting the laser beams from the laser array by one of thereflection surfaces, and the focusing optical system focusing thedeflected laser beams from the rotary deflector onto the scanned surfaceto form the beam spots thereon.
 3. The multi-beam scanning device ofclaim 1 wherein the semiconductor laser array is configured such thatthe inclination angle of the light emitting parts is equal to
 0. 4. Themulti-beam scanning device of claim 1 wherein the semiconductor laserarray is configured such that the inclination angle of the lightemitting parts is larger than
 0. 5. The multi-beam scanning device ofclaim 2 wherein the coupling lens is configured to convert the laserbeams emitted by the semiconductor laser array into parallel laserbeams.
 6. The multi-beam scanning device of claim 2 wherein the lightemitting parts of the semiconductor laser array emit divergent laserbeams, and the coupling lens is configured to convert the laser beamsemitted by the semiconductor laser array into less divergent laserbeams.
 7. The multi-beam scanning device of claim 2 wherein the rotarydeflector comprises a rotary polygonal mirror, the rotary polygonalmirror being rotated at a constant speed around a rotation axis of therotary polygonal mirror, which allows the scanned surface to be scannedat a constant speed in the main scanning direction with the beam spots.8. The multi-beam scanning device of claim 5 wherein the rotarydeflector comprises a rotary polygonal mirror and the focusing opticalsystem comprises an fθ lens.
 9. The multi-beam scanning device of claim2 wherein the line focusing lens comprises a cylindrical lens.
 10. Themulti-beam scanning device of claim 4 wherein the semiconductor laserarray is configured such that the inclination angle of the lightemitting parts is larger than 0 and approximately equal to 90, themulti-beam scanning device further comprising a main-scanning-directionbeam expander provided between the coupling lens and the rotarydeflector, the beam expander enlarging the diameter of the laser beams,passed through the coupling lens, in the main scanning direction.
 11. Alight source device for use in a multi-beam scanning device, the lightsource device comprising: a semiconductor laser array having a pluralityof light emitting parts emitting multiple laser beams; a coupling lenscoupling the laser beams emitted by the laser array; and an aperturestop restricting a diameter of the laser beams passed through thecoupling lens, wherein the multi-beam scanning device comprising: thelight source device; a rotary deflector deflecting the laser beamsemitted by the light emitting parts of the laser array; and a focusingoptical system focusing the deflected laser beams from the rotarydeflector onto a scanned surface to form a plurality of beam spots thatare separated on the scanned surface in a sub-scanning direction, thescanned surface being scanned simultaneously with the plurality of beamspots in a main scanning direction by a rotation of the rotarydeflector, wherein the laser array is configured such that the lightemitting parts are arrayed along a line that is at an inclination angleφ to the sub-scanning direction, the inclination angle φ measured indegrees and meeting the condition 0≦0<90, and that a scanning line pitchP, an array pitch ρ of the light emitting parts of the laser array and aparameter K defined by the equation K=0.82 λ/ωz, where λ is a wavelengthof the emitted laser beams and ωz is a target beam spot diameter in thesub-scanning direction, satisfy the following conditions:0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0.030 and wherein the aperture stop isconfigured to have a numerical aperture NAzS in the sub-scanningdirection that satisfies the conditions: 0.01<NAzS<0.
 30. 12. The lightsource device of claim 11 wherein the semiconductor laser array isconfigured such that the inclination angle of the light emitting partsis equal to
 0. 13. The light source device of claim 11 wherein thesemiconductor laser array is configured such that the inclination angleφ of the light emitting parts is larger than
 0. 14. The light sourcedevice of claim 1 1 wherein the coupling lens is configured to convertthe laser beams emitted by the semiconductor laser array into parallellaser beams.
 15. The light source device of claim 14 wherein thecoupling lens comprises a single lens.
 16. The light source device ofclaim 11 wherein the light emitting parts of the semiconductor laserarray emit divergent laser beams, and the coupling lens is configured toconvert the laser beams emitted by the semiconductor laser array intoless divergent laser beams.
 17. The light source device of claim 11wherein the semiconductor laser array is configured such that the arraypitch ρ of the light emitting parts is equal to 10 μm.
 18. The lightsource device of claim 11 wherein the semiconductor laser array isconfigured such that the wavelength λ of the emitted laser beams isbelow 700 nm.
 19. A multi-beam scanning method comprising the steps of:providing a semiconductor laser array having a plurality of lightemitting parts emitting multiple laser beams; providing a rotarydeflector deflecting the laser beams emitted by the light emitting partsof the semiconductor laser array; focusing the deflected laser beamsfrom the rotary deflector onto a scanned surface to form a plurality ofbeam spots that are separated on the scanned surface in a sub-scanningdirection; and scanning the scanned surface simultaneously with theplurality of beam spots in a main scanning direction by a rotation ofthe rotary deflector; wherein the laser array is configured such thatthe light emitting parts are arrayed along a line that is at aninclination angle φ to the sub-scanning direction, the inclination angleφ measured in degrees and meeting the conditions 0≦φ<90, and that ascanning line pitch P, an array pitch ρ of the light emitting parts ofthe laser array and a parameter K defined by the equation K=0.82 λ/ωz,where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions: 0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0.030.
 20. An image formingapparatus in which a multi-beam scanning device is provided, the imageforming apparatus forming an electrostatic latent image on a scannedsurface of a photosensitive medium through an exposure of thephotosensitive medium to an imaging light pattern provided by themulti-beam scanning device, the multi-beam scanning device comprising: asemiconductor laser array having a plurality of light emitting partsemitting multiple laser beams; a rotary deflector deflecting the laserbeams emitted by the light emitting parts of the semiconductor laserarray; and a focusing optical system focusing the deflected laser beamsfrom the rotary deflector onto a scanned surface to form a plurality ofbeam spots that are separated on the scanned surface in a sub-scanningdirection, the scanned surface being scanned simultaneously with theplurality of beam spots in a main scanning direction by a rotation ofthe rotary deflector, wherein the laser array is configured such thatthe light emitting parts are arrayed along a line that is at aninclination angle φ to the sub-scanning direction, the inclination angleφ measured in degrees and meeting the conditions 0≦φ<90, and that ascanning line pitch P, an array pitch ρ of the light emitting parts ofthe laser array and a parameter K defined by the equation K=0.82 λ/ωz,where λ is a wavelength of the emitted laser beams and ωz is a targetbeam spot diameter in the sub-scanning direction, satisfy the followingconditions: 0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0.
 030. 21. The imageforming apparatus of claim 20 wherein the photosensitive medium is aphotoconductive drum, and the image forming apparatus uniformly chargesthe photoconductive drum and exposes the photoconductive drum to theimaging light pattern provided by the multi-beam scanning device, sothat the electrostatic latent image is formed on the scanned surface ofthe photoconductive drum, and the image forming apparatus developing thelatent image of the photoconductive drum with toner and transferring atoned image from the photoconductive drum to a copy sheet.
 22. Amulti-beam scanning device comprising: semiconductor laser array meanshaving a plurality of light emitting parts for emitting multiple laserbeams; rotary deflector means for deflecting the laser beams emitted bythe light emitting parts of the laser array means; and focusing opticalmeans for focusing the deflected laser beams from the rotary deflectormeans onto a scanned surface to form a plurality of beam spots that areseparated on the scanned surface in a sub-scanning direction, thescanned surface being scanned simultaneously with the plurality of beamspots in a main scanning direction by a rotation of the rotary deflectormeans, wherein the laser array means is configured such that the lightemitting parts are arrayed along a line that is at an inclination angleφ to the sub-scanning direction, the inclination angle φ measured indegrees and meeting the conditions 0≦φ<90, and that a scanning linepitch P, an array pitch ρ of the light emitting parts of the laser arraymeans and a parameter K defined by the equation K=0.82 λ/ωz, where λ isa wavelength of the emitted laser beams and ωz is a target beam spotdiameter in the sub-scanning direction, satisfy the followingconditions: 0.01<K·P/(ρ·cos φ)<0.30 0.011<K<0. 030.